\newcommand{\R}{\mathbb{R}}
\newcommand{\partial}{\partialial}
\newcommand{\po}{\boldsymbol}
\newcommand{\mathrm}{\mathop{}\!\mathrm{d}}
\newcommand{\prj}{\mathop{\mathrm{Prj}}}
\newcommand{\diam}{\mathop{\mathrm{diam}}}
\newcommand{\jacobi}{\mathop{J}}
\newcommand{\grad}{\mathop{\mathrm{grad}}}
\newcommand{\fpart}[2]{\frac{\partial{#1}}{\partial{#2}}}
\newcommand{\fppart}[2]{\frac{\partial^2{#1}}{\partial{{#2}^2}}}
\newcommand{\dive}{\mathop{\mathrm{div}}}
\newcommand{\laplace}{\mathop{\Delta}}
\newcommand{\rot}{\mathop{\mathrm{rot}}}
\newcommand{\series}[2]{\sum\limits_{#1=1}^{\infty}#2_#1}
\newcommand{\aseries}[2]{\sum\limits_{#1=1}^{\infty}(-1)^{#1-1}#2_#1}
\newcommand{\Rarr}{\Rightarrow}
\newcommand{\and}{\land}
\newcommand{\exist}{\exists}